Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
R = lambda: map(int, raw_input().split())
n, m = R()
a = [R() for _ in xrange(n)]

rows_first = n <= m
row_name = 'row'
col_name = 'col'

if not rows_first:
    a = map(list, zip(*a))
    row_name, col_name = col_name, row_name
    n, m = m, n

state = [[0] * m for _ in xrange(n)]

def print_m(m):
    print
    for i in m:
        print ' '.join(map(str, i))

moves = []
for row_idx in xrange(n):
    row_moves = min(a[row_idx])
    moves.extend((row_name, row_idx + 1) for i in xrange(row_moves))
    state[row_idx] = [row_moves] * m
    # print_m(state)

for col_idx in xrange(m):
    max_col_state = max(state[i][col_idx] for i in xrange(n))
    max_col = max(a[i][col_idx] for i in xrange(n))
    col_moves = max_col - max_col_state
    if col_moves > 0:
        for row_idx in xrange(n):
            state[row_idx][col_idx] += col_moves

        moves.extend((col_name, col_idx + 1) for i in xrange(col_moves))
    # print_m(state)

if state == a:
    print len(moves)
    for move_name, idx in moves:
        print move_name, idx
else:
    print -1